Previous theoretical work on fast Alfven eigenmodes suggests that it is not possible for any single mode to satisfy boundary conditions in a rectangular cross-section torus, even though such modes are observed experimentally. The authors show that it is possible for fast wave modes to satisfy the boundary conditions, provided that the bulk plasma is separated from the vessel walls by a low-density edge plasma or vacuum region. The boundary conditions can then be satisfied by the presence of poloidally-evanescent wave fields. Toroidal geometry introduces a strong asymmetry in the wavefields between the high- and low-field sides of the torus, but the eigenfrequencies are close to those predicted using a simple cylindrical model.